The cone and the sphere intersect in a circle whose radius is 1, whose center is at , and which lies in the plane . This is established by solving the equations and simultaneously. Since these equations imply , the solutions are easily seen to be and . Each generator of the cone therefore has length .
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The sphere is given in spherical coordinates by , so the plot data-structure houses the graph of the upper hemisphere. The cone is given in spherical coordinates by , so the plot data-structure houses the graph of the cone.